Janke, Wolfhard
Title: Error Estimation and Reduction with Cross Correlations
Authors: Martin Weigel1 and Wolfhard Janke2
Affiliation:
1. University of Mainz, Germany
2. University of Leipzig, Germany
Abstract:
Besides the well-known effect of autocorrelations in time series of Monte Carlo simulation data resulting from the underlying Markov process, using the same data pool for computing various estimates entails additional cross correlations. This effect, if not properly taken into account, leads to systematically wrong error estimates for combined quantities. Using a straightforward recipe of data analysis employing the jackknife or similar resampling techniques, such problems can be avoided. In addition, a covariance analysis allows for the formulation of optimal estimators with often significantly reduced variance as compared to more conventional averages. The basic ideas will be illustrated for finite-size scaling analyses of the two- and three-dimensional Ising model.
M. Weigel and W. Janke, Cross Correlations in Scaling Analyses of Phase Transitions, Phys. Rev. Lett. 102, 100601-1--4 (2009) [arXiv:0811.3097] (see also Phys. Rev. Lett. Highlights Synopsis of April 13, 2009);
M. Weigel and W. Janke, Error Estimation and Reduction with Cross Correlations, Phys. Rev. E81, 066701-1--15 (2010) [arXiv:1002.4517].
Authors: Martin Weigel1 and Wolfhard Janke2
Affiliation:
1. University of Mainz, Germany
2. University of Leipzig, Germany
Abstract:
Besides the well-known effect of autocorrelations in time series of Monte Carlo simulation data resulting from the underlying Markov process, using the same data pool for computing various estimates entails additional cross correlations. This effect, if not properly taken into account, leads to systematically wrong error estimates for combined quantities. Using a straightforward recipe of data analysis employing the jackknife or similar resampling techniques, such problems can be avoided. In addition, a covariance analysis allows for the formulation of optimal estimators with often significantly reduced variance as compared to more conventional averages. The basic ideas will be illustrated for finite-size scaling analyses of the two- and three-dimensional Ising model.
M. Weigel and W. Janke, Cross Correlations in Scaling Analyses of Phase Transitions, Phys. Rev. Lett. 102, 100601-1--4 (2009) [arXiv:0811.3097] (see also Phys. Rev. Lett. Highlights Synopsis of April 13, 2009);
M. Weigel and W. Janke, Error Estimation and Reduction with Cross Correlations, Phys. Rev. E81, 066701-1--15 (2010) [arXiv:1002.4517].